Hadron-Hadron interactions from Nf=2+1+1 lattice QCD: I=3/2 πK scattering length

C Helmes,B Kostrzewa,M Werner,C Jost,L Liu,F Pittler,C Urbach,B Knippschild

doi:10.1103/physrevd.98.114511

Abstract

In this paper we report on results for the s-wave scattering length of the $\pi$-$K$ system in the $I=3/2$ channel from $N_f=2+1+1$ Lattice QCD. The calculation is based on gauge configurations generated by the European Twisted Mass Collaboration with pion masses ranging from about $230$ to $450\,\text{MeV}$ at three values of the lattice spacing. Our main result reads $M_{\pi}\,a_0^{3/2,\text{phys}} = -0.059(2)$. Using chiral perturbation theory we are also able to estimate $M_{\pi}\,a_0^{1/2,\text{phys}} = 0.163(3)$. The error includes statistical and systematic uncertainties, and for the latter in particular errors from the chiral and continuum extrapolations.

Highlights

For understanding the strong interaction sector of the standard model (SM), it is not sufficient to compute masses of stable particles
We report on results for the s-wave scattering length of the π-K system in the I 1⁄4 3=2 channel from Nf 1⁄4 2 þ 1 þ 1 lattice quantum chromodynamics (QCD)
Let us first discuss the main systematics of our computation: In contrast to the pion-pion or kaon-kaon systems, there is time dependent thermal pollution in the correlation functions relevant for the extraction of the pion-kaon s-wave scattering length

Summary

Introduction

For understanding the strong interaction sector of the standard model (SM), it is not sufficient to compute masses of stable particles. Due to the nonperturbative nature of low-energy quantum chromodynamics (QCD), computations of interaction properties from lattice QCD are highly desirable. While the phase shift in a given partial wave is to be computed, the scattering length is in many cases a useful quantity, in particular when the two-particle interaction is weak. Due to the importance of chiral symmetry in QCD the investigation of systems with two pseudoscalar mesons is of particular interest. Chiral perturbation theory (ChPT) is able to provide a description of the pion mass dependence, and any nonperturbative computation, in turn, allows us to check this dependence. ChPT works best for two pion systems, while convergence is unclear for pion-kaon or two kaon systems

Methods

Findings

Discussion

Conclusion